Algebra Examples

$2 = \frac{3}{5} x - \frac{1}{3} x + \frac{2}{5} x$

Step 1

Rewrite the equation as $\frac{3}{5} x - \frac{1}{3} x + \frac{2}{5} x = 2$ .

$\frac{3}{5} x - \frac{1}{3} x + \frac{2}{5} x = 2$

Step 2

Simplify $\frac{3}{5} x - \frac{1}{3} x + \frac{2}{5} x$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Combine $\frac{3}{5}$ and $x$ .

$\frac{3 x}{5} - \frac{1}{3} x + \frac{2}{5} x = 2$

Step 2.1.2

Combine $x$ and $\frac{1}{3}$ .

$\frac{3 x}{5} - \frac{x}{3} + \frac{2}{5} x = 2$

Step 2.1.3

Combine $\frac{2}{5}$ and $x$ .

$\frac{3 x}{5} - \frac{x}{3} + \frac{2 x}{5} = 2$

Step 2.2

Simplify terms.

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Step 2.2.1

Combine the numerators over the common denominator.

$\frac{3 x + 2 x}{5} + \frac{- x}{3} = 2$

Step 2.2.2

Add $3 x$ and $2 x$ .

$\frac{5 x}{5} + \frac{- x}{3} = 2$

Step 2.3

Simplify each term.

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Step 2.3.1

Cancel the common factor of $5$ .

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Step 2.3.1.1

Cancel the common factor.

$\frac{5 x}{5} + \frac{- x}{3} = 2$

Step 2.3.1.2

Divide $x$ by $1$ .

$x + \frac{- x}{3} = 2$

Step 2.3.2

Move the negative in front of the fraction.

$x - \frac{x}{3} = 2$

Step 2.4

To write $x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$x \cdot \frac{3}{3} - \frac{x}{3} = 2$

Step 2.5

Simplify terms.

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Step 2.5.1

Combine $x$ and $\frac{3}{3}$ .

$\frac{x \cdot 3}{3} - \frac{x}{3} = 2$

Step 2.5.2

Combine the numerators over the common denominator.

$\frac{x \cdot 3 - x}{3} = 2$

Step 2.6

Simplify the numerator.

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Step 2.6.1

Move $3$ to the left of $x$ .

$\frac{3 \cdot x - x}{3} = 2$

Step 2.6.2

Subtract $x$ from $3 x$ .

$\frac{2 x}{3} = 2$

Step 3

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot 2$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{3}{2} \cdot \frac{2 x}{3}$ .

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Step 4.1.1.1

Cancel the common factor of $3$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 x}{3} = \frac{3}{2} \cdot 2$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 x) = \frac{3}{2} \cdot 2$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

Factor $2$ out of $2 x$ .

$\frac{1}{2} (2 (x)) = \frac{3}{2} \cdot 2$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 x) = \frac{3}{2} \cdot 2$

Step 4.1.1.2.3

Rewrite the expression.

$x = \frac{3}{2} \cdot 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Cancel the common factor.

$x = \frac{3}{2} \cdot 2$

Step 4.2.1.2

Rewrite the expression.

$x = 3$